For the digital control system given in Figure 3, by adding phantom samplers to showthat the z transfer function of the closed-loop system is given byC(z)R(z)=G1 G2(z)1 + G₁G₂(z)H(z)G₁(s)R(s)H(s)Figure 3[15 marks]G₂(S)C(s)

Answered: For the digital control system given in…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Problem 3. Consider the electrical circuit shown in Figure 3 (left). Assume that R₁ = R2 = 1 and C = 1F. 1) (15 points) Derive the transfer function G(s) = Vo(s)/Vs(s) of the electrical circuit. 2) (15 points) If a controller is used to control the system, then the block diagram of the closed-loop system is given by Fig. 3 (right). Suppose that the reference is a ramp signal, i.e., r(t) = t 1(t). Design a controller De(s) such that the closed-loop system achieves perfect tracking (e(t) = r(t) - y(t) → 0). Justify your design. a -> + US R₁i w C: iz iz i3 + R2 Vo RO Σ Do(s) G(s) OY Figure 3: Electrical system in Problem 3.
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For the digital control system given in Figure 3, by adding phantom samplers to show that the z transfer function of the closed-loop system is given by C(z) R(z) = G1 G2(z) 1 + G₁G₂(z)H(z) G₁(s) R(s) H(s) Figure 3 [15 marks] G₂(S) C(s)